How do you do an intrude instead of extrude?
The answer is to simply just grab all the faces on the bottom of the chair, press G to grab them, and press Z afterwards to pull the faces only vertically. This isn't intruding, but just moving faces. Simply put, drag the faces up without pressing E, in the case of the chair legs. I hope this answers your question!
On another note...
if you press I, then inset faces, and then extrude, moving up into the mesh, it will create a hollow space with depth, rather than just 4 faces with no cap. This second response probably doesn't answer your question, but this is probably what 'Intrude' means in Blender.